Affiliations: [a] School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi, China
| [b] Department of Radiation Oncology, Moffitt Cancer Center, Tampa, FL, USA
| [c] Department of Radiation and Cellular Oncology, University of Chicago, Chicago, IL, USA
Correspondence:
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Correspondence to: Zhiwei Qiao, School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi, China. E-mail: zqiao@sxu.edu.cn and Howard Halpern, Department of Radiation and Cellular Oncology, University of Chicago, Chicago, IL, USA. E-mail: hhalpern@uchicago.edu.
Abstract: BACKGROUND AND OBJECTIVE:Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model. METHODS:The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure. RESULTS:We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model. CONCLUSION:The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.
